Submit a written or typed note with- 1.Name 2. Group number 3. Question number 4. Short reason/explanation stating the reason for re-grading.

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1 Exam 2 rebuttals due Tuesday Submit a written or typed note with- 1.Name 2. Group number 3. Question number 4. Short reason/explanation stating the reason for re-grading. - Homework 7 will be online tomorrow morning - Due in class on Tuesday

2 LB 144: Organismal Biology Class 22 Popula7on Ecology 2

3 Learning Objec-ves Apply the defini7ons of popula7on dynamics to examples. Solve popula7on growth problems using the exponen7al and logis7c growth models. Describe (in words and on a graph) how different life history traits, density dependence, and density independence affect these mathema7cal models.

4 Describing a popula7on 1. Density 2. Dispersion 3. Demography Changes in space and 7me are called dynamics

5 Dynamics Two popula-on growth models: A) Exponen7al Growth (density independent) B) Logis7c Growth (density dependent) 5

6 What factors change the popula7on size of an organism over 7me? Popula7on size (N) 6

7 Change in popula7on size over 7me Births (+) Immigration (+) Emigration (-) Popula7on size (N) Deaths (-) 7

8 WB: Create a word equation that describes the change in population size over time. Births (+) Immigration (+) Emigration (-) Popula7on size (N) ΔN/Δt = Deaths (-) Change in population size over time Copy this equation into your carbonless as Q1

9 Change in popula-on size over -me ΔN= births deaths + immig - emig ΔN = B D Copy this equation as Q2. These are ignored in the mathematical model because they are assumed to be approximately equal, therefore, sum to zero

10 1) ΔN/Δt = (B D) We can calculate these values using to per capita (per individual) values: B = bn D = dn

11 1) ΔN/Δt = (B D) What you is need growth RATE? We can calculate these values using to per capita (per individual) values: B = bn D = dn So can now rearrange to get: 2) ΔN/Δt = bn dn = N(b-d)

12 1) ΔN/Δt = (B D) What you is need growth RATE? We can calculate these values using to per capita (per individual) values: B = bn D = dn So can now rearrange to get: 2) ΔN/Δt = bn dn = N(b-d) (b-d) = r (per capita rate of increase) So now get: 3) ΔN/Δt = rn

13 1) ΔN/Δt = (B D) What you is need growth RATE? We can calculate these values using to per capita (per individual) values: B = bn D = dn So can now rearrange to get: 2) ΔN/Δt = bn dn = N(b-d) (b-d) = r (per capita rate of increase) So now get: 3) ΔN/Δt = rn Copy this equation as Q3.

14 Start with population of 1000 In 1 yr, 100 birth, 50 deaths. b=100/1000=0.1 per capita births d=50/1000=0.05 per capita deaths r = b-d= 0.05 Pop change in 1 year = ΔN/Δt = 0.05*1000=50 Population at time t = 1050 Q4. Starting with 1050 individuals, if r remains constant, calculate population size from year 1 to year 2.

15 1) ΔN/Δt = (B D) What you is need growth RATE? can relate these to per capita values: B = bn D = dn So can now rearrange to get: 2) ΔN/Δt = bn dn = N(b-d) and b-d = r (per capita rate of increase), so now get: 3) ΔN/Δt = rn Copy this equation as Q3. Start with population of 1000 In 1 yr, 100 birth, 50 deaths. b=100/1000=0.1 per capita births d=50/1000=0.05 per capita deaths r = b-d= 0.05 Pop change / 1 yr = ΔN/Δt = 0.05*1000=50 Population at time t = 1050 Q4. Starting with 1050 individuals, if r remains same calculate population size in 1 yr.

16 RECAP ΔN/ Δt = rn If r is nega7ve, popula7on is declining If r is posi7ve, popula7on is increasing If r is 0, popula7on is stable r per capita rate of increase (b-d) i.e. birth rate/ind. death rate/ind.

17 r remains constant, so more individuals are added to the popula7on during each 7me increment ΔN/ Δt = rn Exponen7al Growth

18 1. Exponen-al Growth (Model) ΔN/ Δt = rn Resources are unlimited Per capita growth rate (r) does not change over 7me Density independent growth Rarely occurs

19 When might exponen-al popula-on growth be realis-c? Coloniza7on of new habitat Recovery axer catastrophe Pulse of nutrients Introduced species Diseases moving through a suscep7ble popula7on 19

20 Dynamics KEY informa7on about a popula7on Popula7on growth rate= change in popula7on size over 7me (ΔN/Δt) Two popula7on growth models: 1. Exponen7al Growth (density independent) 2. Logis-c Growth (density dependent)- builds on (1.) but more complicated and realis-c 20

21 2. Logis7c Growth (discrete) Building a be_er model: ΔN/ Δt = rn K-N K What do you recognize? What is new?

22 2. Logis7c Growth (discrete) K = carrying capacity The maximum popula7on that an environment can sustain ΔN/ Δt = rn K-N K

23 2. Logis7c Growth (discrete) This circled phrase = unu7lized opportunity for popula7on growth ΔN/ Δt = rn K-N K Population size Time

24 2. Logis7c Growth (discrete) This circled phrase = unu7lized opportunity for popula7on growth ΔN/ Δt = rn K-N K Q5. Calculate the value of the circled term for K=100 and: a. N t =10 b. N t =90 c. N t =110

25 Q4. Calculate the value of the circled term for K=100 and: a. N t =10 " N = rn t t $ # K N t K % ' & b. N t =90 c. N t =110 How does the circled term change as N gets larger?

26 2. Logistic Growth Resources are limited Carrying Capacity, K Pop. growth rate decreases over time (slows as the population approaches K) Population size Density dependent growth Time 26

27 CQ: For a popula7on that is undergoing logis7c growth and is at K, what is popula7on growth rate? A.0 B.1.0N C.1,500 D.15